Which batterie to use for best laser output

no no, iam not going to mess up with my only laser... but thank you anyway

Then, I would recommend sticking with garden variety AA batteries. Li-ion batteries definitely pack a punch, so I am not going to recommend this at all due to good chance of smoking both driver and diode. Lithium Iron Phosphate may be one acceptable Li-ion battery variery but still we won't know unless the module's taken out and driver chip checked against the datasheet.

Check out lighthound.com they have high quality cells.